4.4. Direction and size of stresses versus shape, material properties, positioning and internal structure
We have found that the leading face of mineralized, radular tooth cusps shows curvatures between 70° and 100° and that during feeding the cusp maintains an upright position with respect to the substrate, thereby maintaining a positive rake angle at least in the earliest phase of its working live. With finite element analysis we have shown that during feeding, thanks to these properties, maximal stresses are generated close to the base of the cusp at the site where the tooth is thickest. This is very advantageous, because here the tooth is strongest and thus less prone to breakage. On the other hand, in a hypothetical tooth with a straight leading edge, the maximal stresses generated during a grazing stroke occur at the very tip where the tooth is thinnest and thus most fragile. Furthermore, maximal stresses were also larger in the tooth with the straight leading edge than in the curved tooth at the same force applied. In conclusion, the presence of a curved leading surface may reduce the speed at which the tooth wears down. We have also shown that, if the rake angle is decreased, the area with maximal stress extends in the direction of the tooth tip. During grazing a tooth in a more reclined position would, therefore, wear down more rapidly than a tooth positioned perpendicular to the substrate. In conclusion, the upright position of chiton and patelloid teeth during grazing is a characteristic, which is optimally fit to reduce the speed at which the teeth wear down.
We have shown that tensile stresses are generated only in the leading part of the tooth and that the direction of maximal tensile stress is parallel to the leading surface. The leading part is also characterized, both in chiton and patelloid mineralized teeth, by the presence of fibres and crystal bundles oriented parallel to the leading surface. Obviously, these fibres and bundles withstand the pull exerted by the maximal stresses generated during grazing, and so add to the strength of the tooth.
We have shown that cracks preferentially propagate along the boundaries of the structural units, which are in a broad sense the fibres, crystal bundles and elongated crystallites making up the internal structure of the tooth. Obviously, breaking of the tooth will most likely occur when compressive forces are applied parallel to the structural units rather than at an angle to them. Comparison of the direction of the structural units (Fig. 2) and the direction of the compressive stresses generated during grazing (Fig. 17) shows that the compressive stresses are parallel to the structural units in the very tip of the tooth only. This means that material losses through breaking will be concentrated to this site of the tooth, which implies that material losses through wearing is minimized.
We have also shown that stresses generated in the trailing part become reduced by increasing the stiffness in the leading part relative to that in the trailing part. This shows that the heterogeneous distribution of elasticity as measured in the real tooth adds to the functionality of the tooth in that it protects the softer materials in the trailing part from being relatively rapidly worn down.
In summary, finite element analysis has made clear that the combination of shape, positioning during feeding, internal structure and material characteristics are highly efficient in reducing wear during the grazing action of the radular tooth.